Joint Source-Channel Coding of Gaussian Sources over Block Erasure Channels: Nonasymptotic Bounds and Channel-Uniform Normal Approximations
Abstract
We study finite-blocklength lossy transmission of a Gaussian memoryless source over memoryless, possibly nonstationary block erasure channels under an excess mean-squared distortion criterion. We derive computable nonasymptotic achievability and converse bounds and establish matching third-order, channel-uniform normal approximations. Our achievability bound exactly evaluates the ensemble-average excess-distortion probability of a specified random coding scheme and improves corresponding specializations of known general one-shot bounds. Our converse conditions on the erasure pattern and source energy and combines spherical-cap and volume bounds, with the spherical-cap term providing the geometric prefactor needed for the matching third-order term. In our channel-uniform normal approximation, we show that for fixed distortion ratio, target excess-distortion probability, and block size, the sufficient and necessary information-balance conditions have the same dispersion and 1/2log k terms, where k is the source blocklength, and differ only by bounded remainders that are uniform over the channel blocklength and erasure-probability profile. Numerical evaluations compare the nonasymptotic JSCC bounds and their common third-order normal approximation with an optimized symmetrized SSCC achievability benchmark.
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BibTeX
@misc{mahmood2026joint,
title = {{Joint Source-Channel Coding of Gaussian Sources over Block Erasure Channels: Nonasymptotic Bounds and Channel-Uniform Normal Approximations}},
author = {Adeel Mahmood},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.38725},
eprint = {2609.38725},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38725},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Joint Source-Channel Coding of Gaussian Sources over Block Erasure Channels: Nonasymptotic Bounds and Channel-Uniform Normal Approximations
AU - Adeel Mahmood
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2609.38725
UR - https://arxiv.org/abs/2609.38725
AB - We study finite-blocklength lossy transmission of a Gaussian memoryless source over memoryless, possibly nonstationary block erasure channels under an excess mean-squared distortion criterion. We derive computable nonasymptotic achievability and converse bounds and establish matching third-order, channel-uniform normal approximations. Our achievability bound exactly evaluates the ensemble-average excess-distortion probability of a specified random coding scheme and improves corresponding specializations of known general one-shot bounds. Our converse conditions on the erasure pattern and source energy and combines spherical-cap and volume bounds, with the spherical-cap term providing the geometric prefactor needed for the matching third-order term. In our channel-uniform normal approximation, we show that for fixed distortion ratio, target excess-distortion probability, and block size, the sufficient and necessary information-balance conditions have the same dispersion and 1/2log k terms, where k is the source blocklength, and differ only by bounded remainders that are uniform over the channel blocklength and erasure-probability profile. Numerical evaluations compare the nonasymptotic JSCC bounds and their common third-order normal approximation with an optimized symmetrized SSCC achievability benchmark.
ER -